Solving spectral problems in piecewise homogeneous media

The problems of finding natural oscillation frequencies of heterogeneous waveguides and intricately shaped membranes are studied. A numerical-and-analytic method is proposed, which consists in developing a solution in each subregion as a series in basis functions followed by matching on the boundary lines. The results of particular computations are presented. Bibliography: 3 titles. Translated fromObchyslyuval’na ta Prykladna Matematyka, No. 76, 1992, pp. 111–118.     

On the superiority of pulsing under a concave advertising market potential function

The authors study the superiority of advertising pulsing policy (turning advertising on and off in a cyclic fashion) over its uniform (constant spending) counterpart that costs the same under the assumption that sales dynamics follow a modified Vidale–Wolfe aggregate advertising model. The authors show that pulsing can be superior if the product of the concave market potential function and the linear or concave advertising response function is convex in advertising. Similar to previous studies in the literature, the average undiscounted profit over the infinite planning horizon is considered as a performance measure according to which alternative advertising pulsation policies are compared.     

Oscillatory integral operators with homogeneous polynomial phases in several variables

We obtain L² decay estimates in λ for oscillatory integral operators Tλ whose phase functions are homogeneous polynomials of degree m and satisfy various genericity assumptions. The decay rates obtained are optimal in the case of (2+2)-dimensions for any m, while in higher dimensions the result is sharp for m sufficiently large. The proof for large m follows from essentially algebraic considerations. For cubics in (2+2)-dimensions, the proof involves decomposing the operator near the conic zero variety of the determinant of the Hessian of the phase function, using an elaboration of the general approach of Phong and Stein [D.H. Phong, E.M. Stein, Models of degenerate Fourier integral operators and Radon transforms, Ann. of Math. (2) 140 (1994) 703-722].     

Optimization of transmission network for homogeneous good market

We examine a model of a perfect competitive homogeneous good market with a network structure. Such a structure is typically important for energy resources: natural gas, oil and electricity. Local markets are connected by transmission lines with limited capacities and given cost functions for capacity increments. We consider the total welfare optimization problem and provide a method that determines optimal investments in the transmission system expansion for some types of the networks. In particular, we study the case where the market is divided into two submarkets with binding transmission line flow constraints between the submarkets. We obtain efficient algorithms for determination of the transmission systems optimal expansion. We conclude with the impact of the results and the outlook to future studies.     

Changing market conditions and advertising strategies: theory and evidence

Using a modified continuous Lanchester model of advertising competition and following a game theoretic approach, this paper investigates analytically the sensitivity of optimal advertising to changes in model parameters in the cases of symmetric and semi-symmetric competition. The theoretical results show that non-dominant firms in both market structures behave similarly whereas the dominant firm in the latter structure behaves considerably differently.We estimate a modified Lanchester model using ready-to-eat cereal data. Based on the obtained estimated parameters, we conduct an empirical analysis to assess the robustness of the theoretical estimated results. In the reported application, we demonstrate that when the model parameters change, non-dominant competitors as well as the dominant rival behave in a manner consistent with the theoretical results related to the semi-symmetric competitive structure.     

Product attraction,advertising and sales: Towards a utility model of market behavior

Summary The purpose of this paper is to develop a theory of household purchasing decisions which are based on utility maximization and are responsive to product attractions. Attractions are defined and are introduced as parameters of the utility function. Alternative specifications are examined, in particular the case of a so-called linear expenditure system. Expenditure and market shares are derived as functions of these attractions. Next, relationships between advertising and attractions are considered. In this way a theoretical basis is found for various ad-hoc-formulae for the relationship between advertising and market share postulated in the marketing literature.

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Zusammenfassung Ziel dieses Aufsatzes ist eine Theorie der Kaufentscheidungen zu entwickeln, die auf der Nutzenmaximierung basiert und zugleich Produktattraktionen anspricht. Attraktionen werden definiert und als Parameter der Nutzenfunktion eingeführt. Alternative Spezifikationen werden untersucht, insbesondere der Fall eines sogenannten linearen Ausgabensystems. Ausgaben und Marktanteile werden als Funktion der Attraktionen abgeleitet. Weiter werden Beziehungen zwischen Werbung und Attraktionen betrachtet. Daraus ergibt sich eine theoretische Begründung für verschiedene ad-hoc-Formeln, die für die Beziehung zwischen Werbung und Marktanteil in der Marktliteratur postuliert worden sind.

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This research was sponsored by grant of Be 272/26 of the German Science Foundation.     

上海股市若干问题分析

借助数学模型探讨股票投资问题.以每日获取最大利润为目标,建立线性规划模型;以市场布林线算法为评价标准划分时期,并建立不同时期的多指标模糊综合评价模型;采用三次指数平滑方法对上证指数进行预测并验证;根据股票价格偏离价值程度图,分析上海股市存在的泡沫情况.     

Optimal media planning for multi-products in segmented market

Promotion is an essential stage of any product life cycle. All firms either concerned with single or multiple products promote their products. Advertising is the most dominated form of promotion for most of the products. Our research focuses on firms which produces a multiple range of products and advertise them using available media options. The budget constraint forms the major restriction. The existing research in media allocation of multiple products ignores the market segmentation and formulates the media plan assuming all segments alike. In this paper we formulate a media planning problem for allocating the available budget in multiple media that are found suitable for the advertising of multiple products considering marketing segmentation aspect of advertising. The objective is to maximize the total reach in all the segments. Goal programming technique is used to solve the problem. A case study is presented to show the real life application of the model.     

The effects of advertising,prices and distribution on market share volatility

Although the influence of marketing decision variables on market share has received ample attention in the literature, less is known about their effects on volatility. This study attempts to shed light on this issue by empirically examining the effects of advertising, pricing and distribution, not only on market share but also on its volatility, using an EGARCH model. We argue that establishing a link between management-controlled actions, such as advertising, pricing and distribution, and market share volatility may benefit firms seeking to reduce uncertainty in their market share performance. Application of the proposed model to data on two markets (SUVs and Minivans), suggested that advertising, pricing and distribution significantly influence market share volatility.     

Existence and uniqueness of a steady state for an OTC market with several assets

We introduce and study a class of over-the-counter market models specified by systems of Ordinary Differential Equations (ODE’s), in the spirit of Duffie-Gârleanu-Pedersen Duffie et al. (Econometrica 73(1):1815–1847, 2005). The key innovation is allowing for multiple assets. We show the existence and uniqueness of a steady state for these ODE’s.     

Modelling advertising budgeting and allocation decisions using modified multinomial logit market share models

Previous research suggests that a multinomial logit model of market share (MNL) is inappropriate for equilibrium analyses of advertising competition. This article shows that when employing simple transformations of the advertising effort, the modified MNL model becomes useful in representing situations of diminishing returns to advertising and appropriate for advertising equilibrium analyses without additional difficulties in its empirical estimation. Using the modified MNL model, optimal advertising budgets together with their allocation over time are derived for both the cases of concave and S-shaped attraction (response) functions in a symmetric oligopoly.     

Sharp Lp decay of oscillatory integral operators with certain homogeneous polynomial phases in several variables

In this paper, we obtain the L~p decay of oscillatory integral operators T_λ with certain homogeneous polynomial phase functions of degree d in(n + n)-dimensions; we require that d 2 n. If d/(d-n) p d/n,the decay is sharp and the decay rate is related to the Newton distance. For p = d/n or d/(d-n), we obtain the almost sharp decay, where "almost" means that the decay contains a log(λ) term. For otherwise, the L~p decay of T_λ is also obtained but not sharp. Finally, we provide a counterexample to show that d/(d-n) p d/n is not necessary to guarantee the sharp decay.     

The estimates of all homogeneous expansions for a subclass of biholomorphic mappings which have parametric representation in several complex variables

In this paper, we obtain the estimates of all homogeneous expansions for a subclass of biholomorphic mappings which have parametric representation on the unit ball of complex Banach spaces.Meanwhile, we also establish the estimates of all homogeneous expansions for the above generalized mappings on the unit polydisk in C~n. Especially, the above estimates are only sharp for biholomorphic starlike mappings and starlike mappings of order α under restricted conditions. Our derived results generalize many known results.     

The boundary-contact problem of elasticity for homogeneous anisotropic media with a contact on some part of the boundaries

The existence and uniqueness of solutions of the boundary-contact problem of elasticity for homogeneous anisotropic media with a contact on some part of their boundaries are investigated in the Besov and Bessel potential classes using the methods of the potential theory and the theory of pseudodifferential equations on manifolds with boundary. The smoothness of the solutions obtained is studied.     

Optimal pricing and advertising in a durable-good duopoly

This paper analyzes dynamic advertising and pricing policies in a durable-good duopoly. The proposed infinite-horizon model, while general enough to capture dynamic price and advertising interactions in a competitive setting, also permits closed-form solutions. We use differential game theory to analyze two different demand specifications – linear demand and isoelastic demand – for symmetric and asymmetric competitors. We find that the optimal price is constant and does not vary with cumulative sales, while the optimal advertising is decreasing with cumulative sales. Comparative statics for the results are presented.     

Random process in a homogeneous Gaussian field

We consider a random process in a spatial-temporal homogeneous Gaussian field V (q , t) with the mean E V = 0 and the correlation function W(|q ? q′|, |t ? t′|) ≡ E[V (q, t)V (q′, t′)], where \( \bold{q} \in {\mathbb{R}^d} \), \( t \in {\mathbb{R}^{+} } \), and d is the dimension of the Euclidean space \( {\mathbb{R}^d} \). For a “density” G(r, t) of the familiar model of a physical system averaged over all realizations of the random field V, we establish an integral equation that has the form of the Dyson equation. The invariance of the equation under the continuous renormalization group allows using the renormalization group method to find an asymptotic expression for G(r, t) as r → ∞ and t → ∞.